%I #3 Mar 30 2012 18:36:57
%S 1,1,1,-1,3,-3,6,-15,58,-64,198,-476,1179,-2907,8377,-19917,69243,
%T -131621,379716,-995100,2878526,-7230486,21469716,-54741166,156719748,
%U -417925683,1220839292,-3221204589,9501389898,-25010664810,73038583431,-197176327311,595340630241
%N Composition of function F = x/(1-x) from functions of the form [x + a(n)*x^n]: F = a(1)*x o x+a(2)*x^2 o x+a(3)*x^3 o ... o x+a(n)*x^n o ...
%e Iterated compositions of [x + a(n)*x^n] forms F = x/(1-x):
%e x/(1-x) = 1x o x+1x^2 o x+1x^3 o x-1x^4 o x+3x^5 o x-3x^6 o x+6x^7 o x-15x^8 o x+58x^9 o x-64x^10 o x+198x^11 o x-476x^12 o...
%e The compositions get closer to F = x/(1-x) at each iteration:
%e (1) 1*x = x;
%e (2) 1*x o x+x^2 = x + x^2;
%e (3) 1*x o x+x^2 o x+1x^3 = x + x^2 + x^3 + 2*x^4 + x^6;
%e (4) 1*x o x+x^2 o x+1x^3 o x-1x^4 =
%e x + x^2 + x^3 + x^4 - 2*x^5 - 2*x^6 - 8*x^7 + x^8 - 3*x^9 +...
%e (5) 1*x o x+x^2 o x+1x^3 o x-1x^4 o x+3x^5 =
%e x + x^2 + x^3 + x^4 + x^5 + 4*x^6 + x^7 + 13*x^8 - 33*x^9 +...
%e (6) 1*x o x+x^2 o x+1x^3 o x-1x^4 o x+3x^5 o x-3x^6 =
%e x + x^2 + x^3 + x^4 + x^5 + x^6 - 5*x^7 + 4*x^8 - 45*x^9 +...
%o (PARI) {a(n)=local(F=x/(1-x+x*O(x^n)),G=x+x*O(x^n));if(n<1,0,if(n==1,polcoeff(F,1), for(k=2,n,c=polcoeff(F/a(1),k)-polcoeff(G,k);G=subst(G,x,x+c*x^k););return(c)))}
%Y Cf. A119459 (decomposition of x/(1-x)).
%K sign
%O 1,5
%A _Paul D. Hanna_, May 20 2006